"I have many / a lot of / lots of things to do today" In this sentence, they all mean the same thing. Perhaps "lots of" sounds a bit more informal. There are some expressions in which it sounds more natural to choose one of them e.g. "I have lots on today" = I have a busy day today (colloquial) "Many people suffer from diabetes" Again you can replace "many" with the other options, but in writing, many sounds more formal and appropriate.

You have to be careful with the uses of "lots of" and "a lot of". They have the exact same meaning but can't always be used in the same place as "many". "Many" ALWAYS refers to an unspecified number of something. They MUST be countable though. Example: Many marbles. In these cases, you can replace "Many" with "lots of" or "a lot of". This doesn't work in cases where the quantity is unspecified AND uncountable. Example: "Lots of water." You CANNOT say "Many water" because "water" is not countable. To reiterate: You can always replace "many" with "lots of" or "a lot of". You can ONLY use "many" if the item mentioned is both of an unspecified quantity AND is not countable. Hope this helps!

Many: * How many cars are in the garage? * There are 100 cars Many, is an amount that can be said with exact numbers. Lot, is that amount can not be expressed in precise numbers.

a lot of = lots of = many + Noun countable (plural)! a lot of = lots of = much + Noun uncountable. For example: I read a lot of/lots of/ many books everyday. I drink a lot of/lots of/ much water everyday. Wish it help!